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A006960
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Reverse and Add! sequence starting with 196.
(Formerly M5410)
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46
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196, 887, 1675, 7436, 13783, 52514, 94039, 187088, 1067869, 10755470, 18211171, 35322452, 60744805, 111589511, 227574622, 454050344, 897100798, 1794102596, 8746117567, 16403234045, 70446464506, 130992928913, 450822227944, 900544455998, 1800098901007, 8801197801088, 17602285712176
(list;
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refs;
listen;
history;
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internal format)
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OFFSET
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0,1
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COMMENTS
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196 is conjectured to be the smallest initial term which does not lead to a palindrome. John Walker, Tim Irvin and others have extended the trajectory of 196 to millions of digits without finding a palindrome.
Palindromes for a(9)/2, a(14)/2 and a(20)/2.
Observed: It seems that most, but not all, Lychrel numbers (seeds given in A063048) have a trajectory term that, divided by 2, becomes palindromic. Note that 196 is the first Lychrel number (A063048(1)). (End)
Observed: On average, 0.414 digits are gained by each step of the reverse and add procedure; i.e., 2.416 steps are needed on average to gain a factor of 10. This holds for any trajectory of reverse and add for decimal number representation. - A.H.M. Smeets, Feb 03 2019
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 196, p. 58, Ellipses, Paris 2008.
D. H. Lehmer, "Sujets d'étude. No. 74," Sphinx (Bruxelles), 8 (1938), 12-13. (This is the currently earliest known reference to the 196 Problem). - James D. Klein, Apr 09 2012.
Daniel Lignon, Dictionnaire de (presque) tous les nombres entiers, Ellipses, Paris, 2012, 702 pages. See Entry 196.
Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 70.
Popular Computing (Calabasas, CA), The 196 Problem, Vol. 3 (No. 30, Sep 1975), pages PC30-6 to PC30-9.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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R. K. Guy, What's left?, Math Horizons, Vol. 5, No. 4 (April 1998), pp. 5-7.
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FORMULA
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EXAMPLE
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Start with 196 = a(0), then:
A056964(196) = 196 + 691 = 887 = a(1); then:
A056964(887) = 887 + 788 = 1675 = a(2); then:
A056964(1675) = 1675 + 5761 = 7436 = a(3); then:
A056964(7436) = 7436 + 6347 = 13783 = a(4); then:
A056964(13783) = 13783 + 38731 = 52514 = a(5); etc. (End)
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 196, (h-> h+ (s->
parse(cat(s[-i]$i=1..length(s))))(""||h))(a(n-1)))
end:
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MATHEMATICA
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a = {196}; For[i = 2, i < 26, i++, a = Append[a, a[[i - 1]] + ToExpression[ StringReverse[ToString[a[[i - 1]]]]]]]; a
NestList[#+FromDigits[Reverse[IntegerDigits[#]]]&, 196, 25] (* Harvey P. Dale, Jun 05 2011 *)
NestList[#+IntegerReverse[#]&, 196, 25] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 04 2019 *)
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PROG
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(Haskell)
a006960 n = a006960_list !! n
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CROSSREFS
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KEYWORD
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nonn,base,nice,easy
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AUTHOR
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EXTENSIONS
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More terms from Vit Planocka (planocka(AT)mistral.cz), Sep 28 2002
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STATUS
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approved
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